A subset of an ambient set in which a notion of connectivity is defined, in the sense of which this subset is connected. For example, connected sets in the space of real numbers are convex sets, and only them; a connected set of a graph is a set in which any two points can be joined by a path that lies entirely in this set. Cf. Connected space.
Connected set. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Connected_set&oldid=31025